Common Core State Standards for Mathematics

4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

This interactive Java applet allows users to explore many types of polyhedra including the Platonic and Archimedean solids, as well as prisms and pyramids among other more advanced shapes. The shape can be rotated and viewed as a solid or a frame. Other tabs allow the user to use slider bars to animate cutting, unfolding to form nets, and other modeling options including truncating the shape. A link is also provided for a printable net of the shape. The resource loads on PC's only.

This lesson helps students develop spatial visualization skills and geometric understanding by exploring the different nets that can be folded into a cube. The lesson is placed in the context of a young woman who is trying to build a jewelry box. The lesson provides an activity sheet, a link to a helpful applet (Cube Nets, cataloged separately), questions for students and teachers, and ideas for assessment and extensions.

This interactive applet helps students develop spatial visualization skills and geometric understanding in both two and three dimensions. From an array of possible nets, students try to select the ones that actually fold to a cube. The applet supports the lesson Building a Box (cataloged separately). An animation that shows one net being folded is included.

This Cyberchase iOS geometry app ($) enables students to use 2D nets to create 3D shapes. The app includes eight levels which increase in difficulty; increasing the complexity of the nets and combining different 3D shapes together.

This narrative document describes the progression of Geometry across the K-6 grade band. It is informed both by research on children's cognitive development and by the logical structure of mathematics. The document discusses the most important goals for elementary geometry in three categories, namely, geometric shapes and their categories, composing and decomposing geometric shapes, and spatial relations and spatial structuring.

Explore geometric solids and their properties with these interactive tools, beginning with an introduction to the faces of basic polyhedra; counting the number of faces, edges, and corners (vertices) in various solids; discovering Euler's Formula; constructing physical models of geometric solids; and identifying which geometric solids can be made from given nets.

In this 4-lesson unit, students identify, compare, and analyze attributes of two- and three-dimensional shapes, and develop geometric vocabulary. Students use basic linear measurement, understand and create scale representations, and explore perimeter and area measurement as they design their clubhouses. Activity sheets (pdf), lesson extensions and other commentary are provided.

This interactive Java applet allows users to investigate surface area and volume of rectangular and triangular prisms by dynamically changing each of the three dimensions with a slider bar. In Explore mode users change the dimensions and view the effect on the prism and on the measures of surface area and volume. In Compute mode, the applet randomly displays a prism and the user computes its surface area and volume. Options include prism type, viewing angle, several 3D drawing options, and an optional scoring feature that tracks the number correct.

This interactive Java applet supports students investigating the folded box problem (maximizing the volume of a rectangular prism). Learners drag corner cutouts, and watch the animated box fold up. The dimensions and the volume and surface area are reported. Ten different grid sheets can be used.

This 3-lesson unit provides students with activities that help them relate solid objects to their 2-D sketches and nets. They will observe and describe attributes and parts of 3-D objects, use hands on materials and interactive websites. They will create and assemble 2-D nets and use Venn diagrams to compare properties. Teacher support materials and student worksheets are provided.